The main utilitarian argument for the death penalty is that it can be a deterrent for serious crimes. If people think they are likely to die as a result of committing a crime, they might be less likely to commit it. This argument is controversial, as the evidence for the effectiveness of capital punishment in deterring crimes is disputed and contradictory at best. Another utilitarian argument would be that the convicted felon is not capable of committing a crime again, because, of course, they are dead. But even this is debated, because the process of appeals that most agree must be navigated in order to provide due process for the convicted person can be even more expensive than housing the criminal for life with almost no chance for escape. (Moral objections or arguments for the death penalty are not really relevant to utilitarian debates.) As for Arizona having the death penalty when others do not, the only way one could argue on utilitarian grounds would be if crime is more of a problem in Arizona than elsewhere. The main argument for Arizona's ability to administer the death penalty when other states do not would be constitutional, involving the power of states to regulate their own criminal justice systems.
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